# Complexity in Software

P u r e T h e o r y
Complexity in Software
Many people underestimate the complexity of software. Software, they argue, is simply a set of
instructions which a computer must follow to carry out a task. Software however can be
unbelievably complex and as, Bruce Sterling puts it, 'protean' or changeable.
For example, the "Savings Account" application pictured at
right is a simple application written in Visual Basic which
performs simple calculations for an investment. To use the
application the user simply fills in three of four of the
possible fields and clicks "Calculate". The program then
works out the fourth variable.
If we look at the input space alone we can work out its
size and hence the number of tests required to achieve
"complete" coverage or confidence it works.
Each field can accept a ten digit number. This means that
for each field there are 10
10
possible combinations of
integer (without considering negative numbers). Since
there are four input fields this means the total number of
possible combinations is 10
40
.
If we were to automate our testing such that we could
execute 1000 tests every second, it would take approximately 3.17x10
29
years to complete testing.
That's about ten billion, billion times the life of the universe.
An alternative would be to seek 100% confidence through 100% coverage of the code. This would
mean making sure we execute each branch or line of code during testing. While this gives a much
higher confidence for much less investment, it does not and will never provide a 100% confidence.
Exercising a single pass of all the lines of code is inadequate since the code will often fail only for
certain values of input or output. We need to therefore cover all possible inputs and once again
we are back to the total input space and a project schedule which spans billions of years.
There are, of course, alternatives.
When considering the input space we can use "equivalence partitioning". This is a logical process
by which we can group "like" values and assume that by testing one we have tested them all. For
example in a numerical input I could group all positive numbers together and all negative numbers
separately and reasonably assume that the software would treat them the same way. I would
probably extend my classes to include large numbers, small numbers, fractional numbers and so on
but at least I am vastly reducing the input set.
Note however that these decisions are made on the basis of our assumed knowledge of the
software, hardware and environment and can be just as flawed as the decision a programmer
makes when implementing the code. Woe betide the tester who assumes that 2
64
-1 is the same as
2
64
and only makes one test against them!
41